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Area in Geometry

Source: 2000 National High School Mathematics League, Exam Two, Problem 1

March 11, 2020
geometrycircumcircle

Problem Statement

In acute triangle ABCABC, D,ED,E are two points on side BCBC, satisfying that ∠BAE=∠CAF\angle BAE=\angle CAF. FM⊥AB,EN⊥ACFM\perp AB,EN\perp AC (M,NM,N are foot points). AEAE intersects the circumcircle of △ABC\triangle ABC at DD. Prove that the area of △ABC\triangle ABC and quadrilateral AMDNAMDN are equal.
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